text: NMR techniques are typically used to predict permeability for fluid typing and to obtain formation porosity, which is independent of mineralogy. The former application uses a surface-relaxation mechanism to relate
  measured relaxation spectra with surface-to-volume ratios of pores, and the latter is used to estimate permeability. The common approach is based on the model proposed by Brownstein and Tarr. They have shown that, in the fast diffusion limit, given by the expression:
  where  is the surface relaxivity of pore wall material,  is the radius of the spherical pore and  is the bulk diffusivity. The connection between NMR relaxation measurements and petrophysical parameters such as permeability stems from the strong effect that the rock surface has on promoting magnetic relaxation. For a single pore, the magnetic decay as a function of time is described by a single exponential:
  where  is the initial magnetization and the transverse relaxation time  is given by:
   is the surface-to-volume ratio of the pore,  is bulk relaxation time of the fluid that fills the pore space, and  is the surface relaxation strength. For small pores or large , the bulk relaxation time is small and the equation can be approximated by: 
  Real rocks contain an assembly of interconnected pores of different sizes. The pores are connected through small and narrow pore throats (i.e. links) that restrict interpore diffusion. If interpore diffusion is negligible, each pore can be considered to be distinct and the magnetization within individual pores decays independently of the magnetization in neighbouring pores. The decay can thus be described as:
  where  is the volume fraction of pores of size  that decays with relaxation time . The multi-exponential representation corresponds to a division of the pore space into  main groups based on  (surface-to-volume ratio) values. Due to the pore size variations, a non-linear optimization algorithm with multi-exponential terms is used to fit experimental data.  Usually, a weighted geometric mean, , of the relaxation times is used for permeability correlations:
   is thus related to an average  or pore size. Commonly used NMR permeability correlations as proposed by Dunn et al. are of the form:
  where  is the porosity of the rock. The exponents  and  are usually taken as four and two, respectively. Correlations of this form can be rationalized from the Kozeny–Carman equation:
  by assuming that the tortuosity  is proportional to . However, it is well known that tortuosity is not only a function of porosity. It also depends on the formation factor . The formation factor can be obtained from resistivity logs and is usually readily available. This has given rise to permeability correlations of the form:
  Standard values for the exponents  and , respectively. Intuitively, correlations of this form are a better model since it incorporates tortuosity information through .
  The value of the surface relaxation strength  affects strongly the NMR signal decay rate and hence the estimated permeability. Surface relaxivity data are difficult to measure, and most NMR permeability correlations assume a constant . However, for heterogeneous reservoir rocks with different mineralogy,  is certainly not constant and surface relaxivity has been reported to increase with higher fractions of microporosity. If surface relaxivity data are available it can be included in the NMR permeability correlation as